Robust Standard Errors for Robust Estimators
AbstractA regression estimator is said to be robust if it is still reliable in the presence of outliers. On the other hand, its standard error is said to be robust if it is still reliable when the regression errors are autocorrelated and/or heteroskedastic. This paper shows how robust standard errors can be computed for several robust estimators of regression, including MMestimators. The improvement relative to non-robust standard errors is illustrated by means of large-sample bias calculations, simulations, and a real data example. It turns out that non-robust standard errors of robust estimators may be severely biased. However, if autocorrelation and heteroscedasticity are absent, non-robust standard errors are more e.cient than the robust standard errors that we propose. We therefore also present a test of the hypothesis that the robust and non-robust standard errors have the same probability limit.
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Bibliographic InfoPaper provided by Katholieke Universiteit Leuven, Centrum voor Economische Studiën in its series Center for Economic Studies - Discussion papers with number ces0316.
Date of creation: Mar 2003
Date of revision:
robust regression; robust standard errors; autocorrelation; heteroskedasticity;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-04-12 (All new papers)
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- Matías Salibián-Barrera & Stefan Aelst & Gert Willems, 2008. "Fast and robust bootstrap," Statistical Methods and Applications, Springer, vol. 17(1), pages 41-71, February.
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